/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 a(a(x1)) -> a(b(x1))
 a(c(x1)) -> b(x1)
 b(b(x1)) -> c(b(a(x1)))

Proof:
 String Reversal Processor:
  a(a(x1)) -> b(a(x1))
  c(a(x1)) -> b(x1)
  b(b(x1)) -> a(b(c(x1)))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(a(x1))
    c#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> a#(b(c(x1)))
   TRS:
    a(a(x1)) -> b(a(x1))
    c(a(x1)) -> b(x1)
    b(b(x1)) -> a(b(c(x1)))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(a(x1))
     c#(a(x1)) -> b#(x1)
     b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> b#(c(x1))
     b#(b(x1)) -> a#(b(c(x1)))
    TRS:
     a(a(x1)) -> b(a(x1))
     c(a(x1)) -> b(x1)
     b(b(x1)) -> a(b(c(x1)))
    graph:
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(x1)
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> b#(c(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(x1)) -> b(a(x1))
      c(a(x1)) -> b(x1)
      b(b(x1)) -> a(b(c(x1)))
     interpretation:
      [c#](x0) = x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = x0 + 0,
      
      [c](x0) = x0 + 0,
      
      [b](x0) = 1x0 + 3,
      
      [a](x0) = 1x0 + 3
     orientation:
      a#(a(x1)) = 1x1 + 3 >= 1x1 + 3 = b#(a(x1))
      
      c#(a(x1)) = 1x1 + 3 >= x1 = b#(x1)
      
      b#(b(x1)) = 1x1 + 3 >= x1 = c#(x1)
      
      b#(b(x1)) = 1x1 + 3 >= x1 + 0 = b#(c(x1))
      
      b#(b(x1)) = 1x1 + 3 >= 1x1 + 3 = a#(b(c(x1)))
      
      a(a(x1)) = 2x1 + 4 >= 2x1 + 4 = b(a(x1))
      
      c(a(x1)) = 1x1 + 3 >= 1x1 + 3 = b(x1)
      
      b(b(x1)) = 2x1 + 4 >= 2x1 + 4 = a(b(c(x1)))
     problem:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(a(x1)) -> b(a(x1))
       c(a(x1)) -> b(x1)
       b(b(x1)) -> a(b(c(x1)))
     Restore Modifier:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(a(x1)) -> b(a(x1))
       c(a(x1)) -> b(x1)
       b(b(x1)) -> a(b(c(x1)))
      EDG Processor:
       DPs:
        a#(a(x1)) -> b#(a(x1))
        b#(b(x1)) -> a#(b(c(x1)))
       TRS:
        a(a(x1)) -> b(a(x1))
        c(a(x1)) -> b(x1)
        b(b(x1)) -> a(b(c(x1)))
       graph:
        b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(a(x1)) -> b(a(x1))
         c(a(x1)) -> b(x1)
         b(b(x1)) -> a(b(c(x1)))
        interpretation:
         [b#](x0) = [0 0]x0 + [0],
         
         [a#](x0) = [2 0]x0 + [0],
         
                   [0  -&]     [0 ]
         [c](x0) = [0  -&]x0 + [-&],
         
                   [0 0]     [0]
         [b](x0) = [2 0]x0 + [3],
         
                   [2 0]     [3]
         [a](x0) = [2 0]x0 + [0]
        orientation:
         a#(a(x1)) = [4 2]x1 + [5] >= [2 0]x1 + [3] = b#(a(x1))
         
         b#(b(x1)) = [2 0]x1 + [3] >= [2  -&]x1 + [3] = a#(b(c(x1)))
         
                    [4 2]     [5]    [2 0]     [3]           
         a(a(x1)) = [4 2]x1 + [5] >= [4 2]x1 + [5] = b(a(x1))
         
                    [2 0]     [3]    [0 0]     [0]        
         c(a(x1)) = [2 0]x1 + [3] >= [2 0]x1 + [3] = b(x1)
         
                    [2 0]     [3]    [2  -&]     [3]              
         b(b(x1)) = [2 2]x1 + [3] >= [2  -&]x1 + [3] = a(b(c(x1)))
        problem:
         DPs:
          b#(b(x1)) -> a#(b(c(x1)))
         TRS:
          a(a(x1)) -> b(a(x1))
          c(a(x1)) -> b(x1)
          b(b(x1)) -> a(b(c(x1)))
        Restore Modifier:
         DPs:
          b#(b(x1)) -> a#(b(c(x1)))
         TRS:
          a(a(x1)) -> b(a(x1))
          c(a(x1)) -> b(x1)
          b(b(x1)) -> a(b(c(x1)))
         EDG Processor:
          DPs:
           b#(b(x1)) -> a#(b(c(x1)))
          TRS:
           a(a(x1)) -> b(a(x1))
           c(a(x1)) -> b(x1)
           b(b(x1)) -> a(b(c(x1)))
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1